The discovery of novel crystalline compounds by numerical simulation is a major challenge in Materials Science. Also, three families are being studied: compounds consisting of lithium and carbon dioxide; the MxNy nitride phases with M = Mg, Ba, Mo and Zr; the GaPO4 and SiS2 systems. The crystallographic structures are determined in silico using the evolutionary algorithm USPEX coupled with DFT calculations (VASP). The study of polymorphism as a function of pressure is carried out whereas the analysis of structural and electronic properties constitutes the heart of this thesis. Our work clearly presents the effect of pressure on the emergence of unexpected stoichiometries, such as Li2(CO2), MgN4, and BaN10. Some of these hypothetical materials remain stable at atmospheric pressure. It's shown that the addition of the s-block element allows the "polymerization" of the unsaturated molecules CO2 and N2 to be carried out at lower pressures. Thus, oxalate C2O42- polymerizes in an infinite poly-dioxane chain in LiCO2 at 33 GPa; the new Li2CO2 composition presents the ethene like (-O)2C=C(O-)2 motif; N2, N3 and N4 finite chains, N5-pentazolate anions, and N6 rings are identified in the AexNy phases, as well as, infinite covalent (1D) chains stabilized by the alkaline earth cations (Ae); the Ba3N2 compound is a conductive electride at ambient pressure and an insulator above 5 GPa; the ground stable structure of MoN2 has encapsulated N2 units, and is not the MoS2 type arrangement proposed by experimentalists; our predictions coupled with the XRD data allow the elucidation of the GaPO4 structure at 20 GPa.